It is concluded that the sedimentary structure ‘stromatactis’ is a calcite cement-fill of a swarm of labyrinthine cavities developed in marine carbonate muds of Palaeozoic bioherms, commonly with geopetal sediment. Field and petrographic evidence is examined from the Ordovician of Dalarna, Sweden, the Devonian of the Canning Basin, Australia, and of Belgium and the Carboniferous of Lancashire, U.K. In all four occurrences the host microspar encloses masses of radiaxial fibrous calcite with sub-horizontal floors. Following other workers, radiaxial fibrous calcite is regarded as an altered marine cement, a conclusion supported by the presence of overlying geopetal sediments with marine fossils, widespread evidence of early submarine cementation in Palaeozoic mud mounds, isotopic analyses, and the presence of microdolomites. The stromatactis masses are separated from each other by laminae of host biomicrospar, which show discontinuities resembling fractures which are healed with the early marine cement, or filled with marine internal sediments. The fractures are therefore of submarine origin. The evidence points to episodic submarine lithification of the carbonate muds, yielding successive crusts between which cavities were eroded and then filled. The crusts were broken and rotated during bioturbation, differential compaction or shearing during burial.